fläche (x^2)/(x^3-3x), 1/(x^3-3x),2,11

Lösung

fläche

\frac{x ^{2}}{x ^{3} - 3 x}, \frac{1}{x ^{3} - 3 x}, 2, 11

\frac{1}{2} ln (118) + \frac{1}{3} ln (11) - \frac{1}{3} ln (2) - \frac{1}{6} ln (11 + 3) + \frac{1}{6} ln (2 + 3) - \frac{1}{6} ln (11 - 3) + \frac{1}{6} ln (2 - 3)

Dezimale

2.15847 \dots

Schritte zur Lösung

Wenden Sie die Flächenformel an:

\int_{2}^{11} \frac{x}{x ^{2} - 3} - \frac{1}{x ^{3} - 3 x} d x

Löse

\int_{2}^{11} \frac{x}{x ^{2} - 3} - \frac{1}{x ^{3} - 3 x} d x : \frac{1}{2} ln (118) + \frac{1}{3} ln (11) - \frac{1}{3} ln (2) - \frac{1}{6} ln (11 + 3) + \frac{1}{6} ln (2 + 3) - \frac{1}{6} ln (11 - 3) + \frac{1}{6} ln (2 - 3)

Die Fläche ist:

= \frac{1}{2} ln (118) + \frac{1}{3} ln (11) - \frac{1}{3} ln (2) - \frac{1}{6} ln (11 + 3) + \frac{1}{6} ln (2 + 3) - \frac{1}{6} ln (11 - 3) + \frac{1}{6} ln (2 - 3)